When you register a domain name through Loopia, you are the owner. We always list our customers as the registrant (the legal domain owner) in the whois (public domain record), so the domain name belongs to you and not to Loopia.
What ownership means in practice
Being the registrant means you control the domain name. You decide where its name servers (DNS servers) point, you can transfer the domain to another registrar (redelegation) if you wish, and you keep the rights to the name for as long as you renew it.
If you want to verify the ownership details for any domain registered with us, search for it on whois.loopia.com.